Slice the flank steak against the grain into very thin strips and season evenly with sea salt and black pepper.
In a small bowl, whisk together the coconut aminos, water, minced ginger, and arrowroot powder to create the stir-fry sauce.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef strips to the skillet in a single layer and sear without moving for 1-2 minutes to develop a brown crust, then toss and cook for another minute before removing the beef from the pan.
Add the broccoli florets to the same skillet with a small splash of water; cover with a lid for 2 minutes to steam until they are bright green and tender-crisp.
Remove the lid, add the minced garlic, and sauté for 30 seconds until fragrant.
Return the beef to the skillet and pour the prepared sauce over the mixture.
Toss everything together for 1 minute until the sauce thickens into a glossy glaze that coats the beef and broccoli.
Transfer to a plate and garnish with sesame seeds before serving.